Finding probabilities using rules
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Due Mar 9, 3:59 AM EDT
Let A and B be some events defined on the same probability space. Assume we know that P(A)=1/2, P(B)=1/3 and P(A∪B)=2/3. Find P(A∩B) (as a proper fraction).
According to rule of sum of probabilities, P(A∪B)=P(A)+P(B)−P(A∩B). Therefore, P(A∩B)=P(A)+P(B)−P(A∪B)=1/2+1/3−2/3=1/6.
A fair dice rolled three times. What is the probability that "6" occurred at least once during this rollings?
Complement event is "6" never occurred. Its probability is 53/63. The probablity of our event is 1−53/63=91/216.